\contentsline {begintocitem}{}{}{}
\contentsline {jobname}{Figueroa}{}{}
\contentsline {doi}{0004/0000.0000}{}{}
\contentsline {arxiv}{math.PR/0000004}{}{}
\contentsline {title}{Nonparametric Estimation for L\unhbox \voidb@x \bgroup \let \unhbox \voidb@x \setbox \@tempboxa \hbox {e\global \mathchardef \accent@spacefactor \spacefactor }\accent 19 e\egroup \spacefactor \accent@spacefactor vy Models Based on Discrete-Sampling}{117}{}
\contentsline {author}{Jos\'e E. Figueroa-L\'opez }{118}{}
\contentsline {endtocitem}{}{}{}
\contentsline {section}{\numberline {1}Introduction}{118}{section.1}
\contentsline {subsection}{\numberline {1.1}Motivation and Some Background}{118}{subsection.1.1}
\contentsline {subsection}{\numberline {1.2}The Statistical Problems and Methodology}{120}{subsection.1.2}
\contentsline {subsection}{\numberline {1.3}An Overview of the Estimators and the Results}{121}{subsection.1.3}
\contentsline {subsection}{\numberline {1.4}Outline}{123}{subsection.1.4}
\contentsline {section}{\numberline {2}The Estimators and Central Limit Theorems}{124}{section.2}
\contentsline {section}{\numberline {3}The Model Selection Problem}{126}{section.3}
\contentsline {subsection}{\numberline {3.1}Analysis of the Variance Term}{127}{subsection.3.1}
\contentsline {subsection}{\numberline {3.2}The Approximation Error for Besov Type Smooth Functions}{129}{subsection.3.2}
\contentsline {subsection}{\numberline {3.3}Rate of Convergence for Smooth Functions Via Splines}{130}{subsection.3.3}
\contentsline {subsection}{\numberline {3.4}About the Critical Mesh}{131}{subsection.3.4}
\contentsline {section}{\numberline {4}Minimax Risk of Estimation for Smooth L\'evy Densities}{132}{section.4}
\contentsline {section}{\numberline {5}A Data-Driven Selection Method and Adaptability}{133}{section.5}
\contentsline {section}{\numberline {6}An Example: Estimation of Variance Gamma Processes.}{134}{section.6}
\contentsline {subsection}{\numberline {6.1}The Model}{134}{subsection.6.1}
\contentsline {subsection}{\numberline {6.2}The Simulation Procedure}{135}{subsection.6.2}
\contentsline {subsection}{\numberline {6.3}The Numerical Results}{136}{subsection.6.3}
\contentsline {section}{Appendix A: Technical Proofs}{137}{section*.3}
\contentsline {section}{Appendix B: Figures}{142}{section*.5}
\contentsline {section}{References}{145}{section*.7}